Stopping the Clock On Retirement: Target Wealth Stopping Time Problems

Abstract

A common approach to retirement planning focuses on building sufficient funds to retire at a fixed, predefined retirement time horizon. Optimal portfolio strategies are applied in an effort to achieve this goal. These strategies typically lead to the wealth at retirement having substantial uncertainty, making it difficult for investors to understand how much to save and how the savings rate impacts their wealth when they retire. A cash investment overcomes these problems, but is generally too expensive for most savers.

Instead, we optimize on statistics of the stopping time at which one has achieved a target wealth. This is related to the notion of labor optionality introduced in "Labor supply flexibility and portfolio choice in a life cycle model", 1992, by Bodie, Merton, and Samuelson, and avoids some of the shortcomings of predefined retirement time approaches.

We solve this retirement stopping time problem using stochastic optimization with a Markov control. The objective function is relatively flat near the optimum, so, for example, reducing both variance and trading frequency have little impact on the optimum. We also prove that shorting strategies are stochastically dominated by ones which do not short, which is of general interest for financial optimization problems.

Keywords: Retirement, pension, portfolio optimization

JEL Classification: G11